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# A New Inverse Square Rule?

Roger Skoff writes Part 1 (of 3) about buying hi-fi and what you pay for it.

It’s the time of year for saving money!

Everybody knows the “Inverse Square Rule” (also called the Inverse Square Law). It’s that thing in physics where for stuff distributing itself from a central point, the amount of it at any point will diminish by a factor of four for every doubling of the distance from that point to the point of origin. Usually it seems to be applied to fields of electromagnetic energy, (light, gravity, magnetism, etc.), but it works just as well for liquids, too: If you have a fixed quantity of water or some other liquid and you pour it into a round pan, starting from any radius or depth of liquid, for every time you double the radius of the pan, you’ll quarter (divide by four) the thickness (depth) of the pool of liquid in the pan.

Now, here’s a surprise: The inverse square rule (or something very much like it) also seems to work (at least after some minimum price point) for buying hi-fi equipment, too, and, as with its more usual applications, it seems to apply equally well going in either direction. For example, and assuming that all other things remain equal: For every doubling of the amount you spend for a new system or component, you’ll get only something like a one-quarter (25%) increase in performance over what you get at the undoubled level. OR, spending half as much for your system or component may get you as much as a four times (400%) increase in performance per dollar spent. Obviously, spending more WILL get you more, but the increase in performance you get will be far less than the increase in price you pay to get it. And, going the other way, spending less will certainly buy you less, but (again, after that certain minimum point) the reduction in performance won’t be anywhere near as great as the reduction in cost.

How can this be? Is it possible, as the trolls and non-comprehenders so constantly bleat, that evil manufacturers and dealers are out to rip off us poor innocent and unsuspecting Hi-Fi Crazies? Or is it because of something else entirely?

The fact of it is a complex mix of physics and economics. Let’s look at the physics part of it first, and let’s start with speakers and the electronics that drive them.

The determining fact of a speaker’s operation is that when you pass a current through any conductor, a magnetic field will form around it. If you then form that conductor into a coil and place it into a high flux-density gap between the poles (or actually one pole and the pole piece) of a magnet, and make the current an AC music signal, the coil will move back and forth in the gap according to the changing polarity and intensity of the driving current. If, finally, you then attach a cone or other diaphragm to the coil, and mount the cone in a suitable frame (the “basket”), you’ll have a loudspeaker, and it will — if the signal driving it is music — play music that will at least be recognizable as such to some degree. How recognizable it is will depend on any number of other factors that we’re not going to go into at this point. The thing that’s significant right now is that, for the overwhelming majority of speakers (electrostatics and some other rarities are different) even though voltage is what allows the current to flow, it’s the current and NOT the voltage that makes the field and supplies the driving force.

Now, consider this: wattage, the actual energy that does the driving, is calculated as Volts times Current, with the current expressed in Amperes (“Amps”), so that the equation can be written as W = VA, and that’s where it starts to get interesting. One watt can be 1 volt x 1 amp = 1 W, or 1000 volts x .001 amp or .001 volts x 1000 amps, or any other combination that comes out to 1. And that means that 1 watt, while it’s always exactly the same total amount of energy, can truly be made up in an infinite number of ways.

Not only that, but, for hi-fi, there seems to be an infinite number of ways to measure it, and that’s where the issue of cost/performance comes in. Despite the fact that even insensitive (inefficient) speakers like my Acoustat 1+1s (which produce only 82 dB @ 1 watt/1 meter) require far less than 1 watt to drive them louder than I might normally want to hear, they need only 2 watts to get them up to the consensus high average listening level of 85 dB reported on one audiophile forum. They can be driven to 95 dB (which is loud) by 20 watts. The fact is that a great many unsophisticated buyers still think that “how many watts it has” is a statement of quality, instead of just how loud an amplifier will drive their speakers.

For that reason it’s not at all unknown for “creative” manufacturers of low-cost gear to find new ways to measure their products that will show them in their most flattering [read “highest output”] light. Among these are rating their amplifiers or receivers into 4 or 6 ohms, instead of the more customary 8. Just this, in itself, will double the truthfully claimable output of most amplifiers or receiver amplifier sections without any other “fudging” needed at all. Another way to truthfully (but generally meaninglessly) rate an amplifier is on its “instantaneous peak power output.” Even if true, just the fact that it’s “instantaneous” means it doesn’t really tell you very much about the amplifier at all.

Just one more way that even a perfectly good-sounding amp can seem to have more power than it really does is by rating it at a higher than usual level of distortion. As long as an amp doesn’t go into “clipping” (which can blow tweeters) it can often continue to be pushed to higher output levels. These will result in more distortion — up to 10% or more, rather than the usual well-under-1-percent, but if they just publish the wattage figure and not the distortion level it was calculated at, how are you going to know? Besides, even if the amplifier claims 100 watts and will only deliver half that much at low distortion, it may still be worth buying at the right price. Remember that even with my Acoustats, 20 watts is still plenty loud, and 50 could be more than you’ll ever use.

One of the ways that high-end amplifiers justify their expense is by avoiding all of the tricks and not only giving you all that they promise, but generally a whole lot more, including a substantial power reserve. They may also use advanced technologies and better components to ensure that you will always get better sound. Think about this: Even taking into consideration the probably quite substantial price difference, which would you rather have? A good used pair of 25-watt Mark Levinson ML2 amplifiers or a brand-new, and even pretty good-sounding, 100-watt-per-channel stereo receiver?

Yup, thought so.

That’s just one example of why better performance can cost disproportionately more to get — and may even emulate something like the inverse square rule in its buyer-impact. I’ll touch on more examples and explore the reasons and their consequences more deeply in the next instalment.

See you next time!

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